Methods and apparatus for obtaining low-dose imaging

ABSTRACT

In one aspect, A method of imaging an object of interest positioned in an exposure area is provided. The method comprises obtaining projection data of the object by providing radiation to the exposure area and detecting at least some of the radiation exiting the object to form the projection data, performing a first reconstruction of the projection data to form at least one bootstrap image, obtaining first data based on information provided by the at least one bootstrap image, and performing a second reconstruction of the projection data based, at least in part, on the first data to form at least one second image.

RELATED APPLICATION

This application is a continuation-in-part (CIP) of U.S. applicationSer. No. 11/595,664 (hereinafter the '664 application) entitled “METHODSAND APPARATUS FOR OBTAINING LOW-DOSE IMAGING,” by Stewart, et al., filedNov. 9, 2006, which in turn claims priority to U.S. ProvisionalApplication Ser. No. 60/735,140, entitled “PLANAR IMAGING METHODS ANDTECHNIQUES,” filed on Nov. 9, 2005, both applications of which areherein incorporated by reference in their entirety.

FIELD OF THE INVENTION

The present invention relates to radiation imaging, and moreparticularly, to obtaining projection data of an object by exposing theobject to radiation from a plurality of view angles.

BACKGROUND OF THE INVENTION

Imaging apparatus that utilize relatively high energy radiation such asx-ray and gamma rays are widely used to obtain images of subject mattermore or less opaque to electromagnetic energy in the visual spectrum.For example, x-ray imaging technology has been employed in a wide rangeof applications from medical imaging to detection of unauthorizedobjects or materials in baggage, cargo or other containers. X-rayimaging typically includes passing radiation (i.e., x-rays) through anobject to be imaged. X-rays from a source passing through the object areattenuated according to the various absorption characteristics of thematerial which the radiation encounters. By measuring the extent ofattenuation of radiation that exits the object (e.g., by comparing theintensity of radiation entering and exiting the object), informationrelated to the density distribution of the object may be obtained.

Computer tomography (CT) techniques typically involve capturing x-rayattenuation information from a plurality of angles about an object beingimaged to reconstruct a three dimensional (3D) volume image of theobject. For example, to obtain attenuation information about an object,a radiation source and a detector (or an array of detectors) responsiveto the radiation may be arranged about the object. Each detector in thearray, for example, may generate an electrical signal proportional tothe intensity of radiation impinging on a surface of the detector. Thesource and detector may be rotated around the object to expose theobject to radiation at a desired number of angular orientations.

At each orientation, referred to as a view angle, the detector signalgenerated by each detector in the array indicates the total absorption(i.e., attenuation) incurred by material substantially in a line betweenthe radiation source and the detector. Therefore, the array of detectionsignals at each view angle records the projection of the object onto thedetector array at the associated view angle. For example, using a 2Ddetector array, the resulting detector signals represent the 2D densityprojection of the object on the detector array at the corresponding viewangle. The signals generated by the detectors form, at least in part,projection data (or view data) of the object.

Projection data obtained from multiple view angles about the object maybe used to compute a density distribution of the object (i.e., todetermine density values for locations within the object). The processof converting projection data (i.e., attenuation as a function of viewangle) to density data (i.e., density as a function of location withinthe object) is referred to as reconstruction. That is, density valuesare reconstructed from information contained in the projection data.Typically, density values are expressed as image data, i.e., pixel orvoxel values in two-dimensional (2D) and three-dimensional (3D) images,respectively.

Many techniques have been developed for reconstructing projection datainto image data. For example, filtered back-projection is a widely usedtechnique to form images from projection data obtained from single ormultiple view angles. In general, reconstruction methods are based uponan assumed relationship between the intensity of radiation impinging ona detector and the integral of the density distribution of the objectalong the line from the radiation source to the detector. For example,the intensity-density relationship of radiation penetrating matter maybe characterized as:I=I ₀e^(−μ(z))  (1),where I₀ is the intensity of the radiation emitted from the radiationsource before penetrating the material, I is the intensity of radiationhaving penetrated the material through a thickness z, and μ is amaterial specific linear absorption coefficient related to the densityof the material. The term “intensity,” with respect to radiation, refersto the amount of radiation present in or passing through a given volumeper unit of time, and is thus a measure of radiation flux. Thedifference between I and I₀ is assumed to be the result of absorption bymaterial substantially along a ray between the radiation sourceproviding the radiation at intensity I and the detector detecting theradiation at intensity I₀. Thus, the relationship in Equation 1 can beused to compute the integral of the μ values over z along the raybetween source and detector. This measurement approximates the totaldensity of material situated along the ray between the source anddetector.

In radiographic images (i.e., images reconstructed from projection dataobtained at a single view angle), the total density approximation may beused as, or may be proportional to, the corresponding pixel value in thereconstructed image. Thus, the appropriate computation may be made alongeach ray from the radiation source to each detector location to form animage of the object at the single view angle. In CT images, projectiondata from multiple view angles are obtained. As a result, the variousrays along which integral μ values are obtained will intersect atdifferent locations within the object, thus providing additionalinformation about discrete μ values at the intersection points.Accordingly, the projection data from multiple view angles may be usedto differentiate individual μ_(i) values along the ray to provideinformation in an additional dimension. That is, rather than having asingle integral μ value along each ray, the information in intersectingrays from the multiple view angles may be correlated to determine μ_(i)values at discrete locations along each ray to provide a tomographicreconstruction of the density distribution.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating some of the effects of scatteredradiation;

FIG. 2 is an illustration of a typical radiation spectrum obtained as afunction of the voltage applied to an x-ray tube;

FIG. 3 is a flowchart illustrating a method for using informationobtained from a bootstrap image to inform a subsequent imagereconstruction, in accordance with some embodiments of the presentinvention;

FIG. 4 is a flowchart illustrating a method for using informationobtained from a bootstrap image to estimate an exit spectrum to inform asubsequent reconstruction, in accordance with some embodiments of thepresent invention;

FIG. 5 is a flowchart illustrating of a method for using informationobtained from a bootstrap image to estimate scattered radiation toinform a subsequent reconstruction, in accordance with some embodimentsof the present invention;

FIG. 6A is a diagram illustrating a method of estimating scatteredradiation from a bootstrap image, in accordance with some embodiments ofthe present invention;

FIG. 6B is a diagram illustrating a method of estimating scatteredradiation from a bootstrap image, in accordance with some embodiments ofthe present invention;

FIG. 7 is a diagram illustrating the use of an anti-scatter grid;

FIG. 8 is a flowchart illustrating a method of using an anti-scattergrid to estimate scattered radiation, in accordance with someembodiments of the present invention;

FIG. 9 is a flowchart illustrating a method of using an estimate ofscattered radiation obtained using an anti-scatter grid at one viewangle to modify projection data obtained at another view angle, inaccordance with some embodiments of the present invention;

FIG. 10 is a diagram of using a proximal density fiducial and a distaldensity fiducial to estimate scattered radiation, in accordance withsome embodiments of the present invention;

FIG. 11 is a diagram illustrating the incorporation of density fiducialsin compression paddles used to position and compress a breast during abreast imaging procedure, in accordance with some embodiments of thepresent invention;

FIG. 12 is a flowchart illustrating a method of using density fiducialsto estimate scattered radiation, in accordance with some embodiments ofthe present invention;

FIG. 13 is a diagram illustrating the use of a substantially opaquedensity fiducial to estimate scattered radiation;

FIG. 14 is a flowchart illustrating a method of using density fiducialsto facilitate identifying a boundary of an object being imaged, inaccordance with some embodiments of the present invention;

FIG. 15 is a flowchart illustrating a method of detecting subjectmotion, in accordance with some embodiments of the present invention;and

FIG. 16 is a diagram of an imaging apparatus suitable for implementingvarious aspects of the present invention.

DETAILED DESCRIPTION

As discussed above, conventional approaches to reconstructing imagesfrom projection data often rely on relatively simple intensity-densityrelationships (e.g., the relationship described above in Equation 1).However, such relationships are oversimplifications of the physicalprocesses occurring as radiation penetrates matter. For example,radiation scattering, beam hardening, diffraction characteristics,spectrum distribution effects, etc., complicate the intensity-densityrelationship. Simplified intensity-density models often assume that allof the radiation intensity detected at a particular detector or detectorlocation is a result of monochromatic transmitted radiation along a raybetween the detector and the radiation source. As such, manyconventional reconstruction methods ignore one or more of the aboveidentified effects, resulting in artifacts in the reconstructed images.

Applicant has appreciated that considering one or more factors notaccounted for in the simplified intensity-density relationship mayfacilitate obtaining higher quality images. In particular, informationabout the one or more factors may be used to modify projection dataand/or to perform more accurate reconstructions, resulting in imagesthat may be more reflective of the actual density distribution of anobject from which the projection data was obtained. There are a numberof factors that may complicate the simplified relationship that may beconsidered, including, but not limited to, radiation scatter and beamhardening, as discussed in further detail below.

Conventional reconstructions based on the simplified intensity-densityrelationship typically assume that radiation is either transmitted orabsorbed along a straight line path between the radiation source and theradiation detector. However, the interaction between penetratingradiation and matter is not such a simple process. Radiation attenuationoccurs as a result of a number of different phenomenon, including thephotoelectric effect, Compton scatter (incoherent scatter), Thompson orRayleigh scattering (coherent scatter), pair production, etc. As aresult, intensity recorded at a detector or detector array may haveresulted from interactions according to various different phenomenon.Accordingly, reconstructions that use the simplifiedintensity-relationship therefore may incorrectly assign density valuesas a result of the assumption that recorded intensity at the detectorsresulted solely from transmitted radiation, as discussed in furtherdetail below.

FIG. 1 is a schematic diagram illustrating the scatter phenomenon andthe effects on image reconstruction using the simplified intensitydensity relationship. In FIG. 1, a radiation source 120 is arranged toprovide radiation to an exposure area 116. For example, radiation source120 may emit a beam of radiation from a source or focal point thatradiates outward in the general shape of a cone. A 2D conic slice of acone beam is illustrated in FIG. 1 (e.g., the conic slice bounded byrays 125 d and 125 e). In particular, radiation source 120 may emitradiation propagating at various angles over the range bounded by rays125 d and 125 e. The cone-beam is directed to irradiate the exposurearea, penetrating objects situated therein. Two exemplary rays 125 a and125 b, along which radiation may propagate, are shown to illustrate thescatter phenomenon.

Object 110 may be positioned in the exposure area such that radiationemitted from radiation source 120 penetrates the object. Duringexposure, a photon traveling along ray 125 a may interact with an atom112 according to the Compton effect. As a result, an electron 133 isejected from the shell of atom 112. In addition, a scattered photon isemitted along ray 125 c. The scattered photon may then be transmittedthrough object 110 to impinge on detector 130 at detector location 132a. Because the simplified model assumes that radiation impinging on thedetector was transmitted along a ray between the radiation source andthe location on the detector at which the radiation was detected, thescattered photon will be treated as if it reached location 132 a alongray 125 b. That is, the reconstruction algorithm will compute densityvalues as if the scattered photon carried information about the densitydistribution along ray 125 b, instead of along rays 125 a and 125 c.Accordingly, failure to take Compton scatter into consideration mayresult in reconstruction errors.

Another factor that complicates the intensity-density relationship isbeam hardening. Beam hardening relates to the phenomenon of preferentialabsorption of radiation energy. In general, radiation provided for thepurpose of obtaining projection data of an object is polychromatic. Thatis, rather than the radiation having a single energy (monochromatic),radiation emitted from a radiation source will have an energydistribution comprising multiple energies. For example, radiation usedin imaging exposures is often generated by directing an electron beam(e-beam) to strike a target surface. Common target materials includetungsten, molybdenum, rhodium, etc. The interaction of the e-beam withthe target surface results in the emission of radiation comprised ofmultiple energies that are dependent on the target material type and theenergy of the e-beam. That is, each target material will emit acharacteristic energy distribution, or spectrum, in response to animpinging e-beam.

The e-beam is often generated in a vacuum tube, and has an energyproportional to a voltage potential between a cathode and anode (thetarget material) of the vacuum tube. As the energy in the e-beamincreases, so does the energy of radiation emitted by the target. Theenergy of radiation is related to the electromagnetic wavelength of theradiation. Accordingly, the higher energy radiation refers to energyhaving shorter wavelengths and lower energy radiation refers toradiation having longer wavelengths. As discussed above, a targetmaterial will emit radiation having a characteristic spectrum as aresult of an e-beam impinging on its surface.

FIG. 2 illustrates the characteristic spectrum of tungsten at a numberof energy levels of an e-beam. In particular, FIG. 2 includes a firstspectrum 205 a, a second spectrum 205 b, a third spectrum 205 c, and afourth spectrum 205 c resulting from bombarding a tungsten target withan e-beam generated at a voltage potential of 80 kilo-volts (kV), 100kV, 120 kV and 140 kV, respectively. The energy spectrum includes twocomponents, the Bremsstrahlung radiation, and the energy peakscharacteristic of the target material. The Bremsstrahlung radiation ischaracterized by the generally continuous distribution of radiation thatincreases in intensity and shifts toward higher frequencies (shorterwavelengths) when the energy of the e-beam is increased. The energypeaks are the characteristic bands shown by the spikes at, for tungsten,59 kilo-electron volts (keV) and 69 keV. As illustrated, increasede-beam energy increases the intensity of the peaks, but may not shiftthe peaks to higher frequencies.

Accordingly, radiation resulting from striking a target with an e-beamhas an energy spectrum that depends, at least in part, on the energy inthe impinging e-beam and the target material type. The energy spectrumof radiation is one factor that impacts the intensity detected at adetector array and complicates the simplified intensity-densityrelationship. Since lower energy radiation is absorbed more easily thanhigher energy radiation, the energy distribution of radiation (i.e., theenergy spectrum) will change as the radiation penetrates matter.

In particular, the proportion of low energy radiation to high energyradiation will be different from the proximal side of the object (i.e.,the side of the object closest to the radiation source) to the distalside of the object (i.e., the side of the object closest to thedetectors). Specifically, the relative proportion of lower radiationwill decrease with the thickness of the material being penetrated,leaving a larger proportion of higher energy radiation impinging on thedetector array. This shift in proportion of higher energy radiation as afunction of penetration depth is referred to as beam hardening.

Beam hardening impacts image reconstruction, in part, because radiationof different energies will react differently with the detector array. Inparticular, higher energy radiation, when absorbed, will generate largerdetector signals than lower energy radiation. As a result, higher energyradiation will be interpreted as higher intensity radiation. Inaddition, higher energy radiation has a higher probability of passingthrough the detector without interacting with the detector lattice.Thus, when monochromatic radiation is assumed, the density valuesreconstructed from the recorded intensities may be incorrect due to theunaccounted for effects of polychromatic radiation.

Furthermore, the detection efficiency of a detector array may be afunction of the energy of the photons in the radiation. For example,higher energy radiation may be detected less efficiently as the higherenergy radiation may penetrate the sensing region of the detectorwithout creating any signal. In addition, lower energy radiation mayalso be detected less efficiently as that radiation energy may fallbelow the threshold for detecting the radiation. Thus, most detectorshave a radiation energy at which they are most efficient, and radiationenergies both lower and higher that that will be detected lessefficiently.

As discussed above, the detector response to radiation of differentenergies is typically a complex function of multiple factors. However,this relationship can generally be determined either experimentally orfrom the known characteristics of the detector. For example, toexperimentally determine the response of the detector to variouswavelengths, a series of measurements using monochromatic radiation atdifferent energies can be used to characterize the response the detectorwill have to the spectrum of energies present in a polychromatic sourceof radiation. Alternatively, the physical properties of the detector canbe used to calculate the response of the detector to radiation ofdifferent energies. For example, some detectors used in x-ray imagingemploy a layer of selenium which is responsible for converting x-rayphotons to electrons. In this case, the known properties of selenium andthe thickness of the selenium can be used to calculate the response ofthe detector to the various energies in a polychromatic source.

As discussed above, projection data obtained from exposing an object toradiation comprises detector signals generated by the detectors inresponse to impinging radiation, the detector signals being indicativeof the intensity of the radiation impinging on the respective detector.However, despite the apparent simplicity of the relationship between thedetector signal and the density distribution of the exposed objectsuggested by Equation 1 (or other generally simplified intensity-densityrelationship models), the detector signals include information about anumber of different factors simultaneously.

First, as indicated by the simplified model, the detector signalsinclude information related to the amount of radiation that wastransmitted through the object to impinge on the detectors. Second, asdiscussed above, the detector signals include information about theamount of radiation that was scattered by the object to impinge on thedetectors. Third, the detector signals are impacted by the energydistribution of the impinging radiation.

However, in conventional imaging, the amount of intensity contributionto the detector signals attributable to each of the factors may not becapable of being separated from each other. That is, absent a prioriinformation about the density distribution of the object, the relativecontributions to the detector signals may not be differentiated, and areoften thus simply ignored or assumed to have resulted from a singlephenomenon. For example, the simplified model performs reconstruction byignoring the second and third effects, e.g., by assuming the detectorsignals result only from monochromatic transmitted radiation.

In a departure from convention, various techniques may be used to obtaininformation that may be used to assist in differentiating the effects ofone or more of the above described factors (e.g., radiation scatter,polychromatic energy spectrum, etc.) on projection data obtained fromexposing an object to radiation. The information may be used to modifyobtained projection data and/or to inform the reconstruction of theprojection data to acquire an image that is more reflective of theactual density distribution within the object.

In some embodiments, one or more bootstrap images (i.e., initialreconstructions of obtained projection data) may be used todifferentiate, to some extent, the intensity contribution attributableto the different factors that influence the detector signals.Information pertaining to the determined contributions may be used toinform a second reconstruction of the projection data to provide a moreaccurate reflection of the density distribution of the object beingimaged. The one or more bootstrap images may be used, for example, todiscriminate contributions attributable to transmitted radiation,scattered radiation and/or a polychromatic spectrum either alone or inany combination.

Information obtained from one or more bootstrap images may be used tomodify projection data and/or inform subsequent reconstructions toimprove image quality in other respects. In some embodiments, projectiondata obtained using an anti-scatter grid may be used to modifyprojection data obtained without using the anti-scatter grid to bothcompensate for and approximate the extent of scattered radiation. Imagesreconstructed from the modified projection data may better characterizethe actual density distribution of the object because scatter effectshave, to some extent, been accounted for.

In some embodiments, one or more density fiducials are positioned nearan object being imaged during exposures, such that informationcorresponding to the density fiducials is present in projection dataobtained from the object, and represented in one or more bootstrapimages. The information in the one or more bootstrap imagescorresponding to the density fiducials may be used to modify theprojection data and/or used to inform a subsequent reconstruction of theprojection data. For example, the one or more density fiducials may beused to estimate scattered radiation, calibrate detector signals and/orassist in identifying a boundary of the object being imaged, such thatsubsequent reconstructions are more reflective of the actual densitydistribution within the object.

Following below are more detailed descriptions of various conceptsrelated to, and embodiments of, methods and apparatus for practicingaspects of the present invention. It should be appreciated that variousaspects of the invention described herein may be implemented in any ofnumerous ways. Examples of specific implementations are provided hereinfor illustrative purposes only. In addition, the various aspects of theinvention addressed in the embodiments below may be used alone or in anycombination, and are not limited to the combinations explicitlydescribed herein.

FIG. 3 illustrates a method of improving image quality by using aninitial image reconstruction (referred to as a bootstrap image) tocharacterize the density distribution of an object exposed to radiationto facilitate modeling one or more penetration effects, in accordancewith some embodiments of the present invention. The term “bootstrapimage” refers herein to an image of any dimensionality that isreconstructed to obtain information that may be used to modifyprojection data and/or to inform a subsequent reconstruction.

Unless otherwise indicated, a bootstrap image may be formed using anytype of reconstruction method, and/or may be a full or only a partialreconstruction of acquired projection data. While a bootstrap image maybe reconstructed according to relatively simple intensity-densityrelationships, the aspects of the invention are not so limited. Inparticular, a bootstrap image may be any collection of image data of anydimensionality (e.g., 2D, 3D, etc.) and may be reconstructed accordingto any desired reconstruction algorithm that transforms projection datainto image data.

In act 310, projection data of an object is obtained from a selectedview angle. For example, an object to be imaged may be exposed toradiation from a first view and the radiation exiting the object may bedetected to collect attenuation information (i.e., projection data) atthe selected view angle.

Act 310 may be repeated for any number of view angles to obtainprojection data at a desired number and configuration views. Forexample, projection data may be obtained by exposing an object toradiation from one or more view angles distributed uniformly ornon-uniformly about the object. U.S. Pat. No. 6,744,848 (hereinafter the'848 patent), entitled “METHOD AND SYSTEM FOR LOW-DOSE THREE-DIMENSIONALIMAGING OF A SCENE,” which is herein incorporated by reference in itsentirety, describes various methods and apparatus for obtainingprojection data of an object from a plurality of view angles in arelatively low dose environment. Any of the methods described in the'848 patent and/or disclosed in the incorporated parent application maybe used to obtain projection data of the object. Other methods ofobtaining projection data may be used as well, as the aspects of theinvention are not limited in this respect.

The projection data may comprise the signal output of a two dimensionalarray of detectors arranged to detect radiation exiting the object. Asdiscussed above, the signal output from each of the detectors may beused as an indication of the integral density of the objectsubstantially along a line between the respective detector and theradiation source. For example, the smaller the detector signal, the moreattenuation is assumed to have occurred along the propagation path ofthe radiation, thus indicating relatively dense material along thecorresponding path. It should be appreciated that other methods ofobtaining projection data may be used, as the aspects of the inventionare not limited in this respect.

In act 320, the projection data obtained from the one or more viewangles is then reconstructed to form image data from the projectiondata. That is, the projection data is transformed into values indicativeof the density distribution of the object. The image reconstructionperformed in act 320 may be performed according to a relatively simpleintensity-density model to provide a bootstrap image. In particular, thedetection signals forming the projection data may be assumed to haveresulted from transmitted monochromatic radiation, and thereforereconstruction may be performed according to Equation 1, for example.

U.S. Pat. No. 5,872,828 (hereinafter the '828 patent), entitled“TOMOSYNTHESIS SYSTEM FOR BREAST IMAGING,” which is herein incorporatedby reference in its entirety, describes various methods forreconstructing a 3D image from projection data obtained from relativelyfew view angles (e.g., using substantially fewer view angles than in CTimaging). Any of the methods described in the '828 patent may be used toreconstruct a 3D image of the projection data obtained from the object.Any other suitable methods of reconstruction may be used, as the aspectsof the invention are not limited in this respect.

As a result of performing simplified image reconstruction in act 320,bootstrap image may include errors associated with scatter and/or beamhardening effects that were not incorporated into the model used toreconstruct the bootstrap image. However, the bootstrap image mayprovide a useable approximation of the density distribution of theobject. Information gleaned from the bootstrap image may then be used todetermine, to some extent, contributions to the detector signals (i.e.,recorded intensity of the radiation impinging on the detectors)attributable to one or more factors such as beam hardening, scatter,etc., and/or to otherwise obtain information that may be used to modifythe projection data and/or inform a subsequent reconstruction.

In act 330, the bootstrap image is processed to glean information aboutthe shape, structure and/or density distribution of the object tofacilitate estimating what portions of the detectors signals resultedfrom any one or combination of penetration effects, and/or to determineother information that may be used to modify the obtained projectiondata and/or inform a second reconstruction of the projection data. Forexample, the density distribution in the bootstrap image may be used toapproximate the exit spectrum to facilitate estimating the contributionto the detector signals from radiation of different energies to accountfor polychromatic effects, as discussed in further detail below inconnection with FIG. 4.

Alternatively, or in addition, the shape of the object may be used toapproximate the contribution to the detector signals from scatteredradiation to account for scatter effects, as discussed in further detailbelow in connection with FIG. 5. It should be appreciated that otherinformation may be extracted from the bootstrap image to facilitatedifferentiating the contributions of various effects on the obtainedprojection data (e.g., effects and contributions not modeled oraccounted for using the simplified transmission model), as the aspectsof the invention are not limited in this respect.

In addition, various methods of distinguishing contributions resultingfrom a respective phenomenon may be used alone or in combination withother methods adapted to differentiate one or more effects arising fromthe interaction between radiation and matter, as the aspects of theinvention are not limited in this respect. Alternatively, or incombination with information relating to various penetration effects,other information may be obtained from the bootstrap image to modify theprojection data and/or inform a second reconstruction. For example, theboundary of the image may be identified to constrain a reconstruction,as described in further detail below.

In act 340, the information gleaned from the bootstrap image is used tomodify the projection data and/or used to constrain, refine or otherwiseinform a second reconstruction of the projection data to form a refinedimage. The second reconstruction, therefore, may incorporate additionaleffects into the computation, thus modeling the intensity-densityrelationship more accurately and/or the reconstruction may be based oninformation about the object that facilitates more accurate assigning ofdensity values. As a result, the refined image resulting from the secondreconstruction may be more reflective of the actual density distributionof the object. It should be appreciated that the second reconstructionmay be performed in any number of ways (e.g., according to any of themethods described in the '828 and/or '848 patents), as the aspects ofthe invention are limited for use to any particular method ofreconstruction.

It should be appreciated that the process can be repeated, resulting incontinued improvement of the reconstructed image. For example, thesecond reconstruction may form an additional bootstrap image from whichinformation is gleaned to inform a further reconstruction. The processof reconstructing bootstrap images to obtain information that informs asubsequent reconstruction may be repeated any number of time (e.g., fora fixed number of times, or until the difference between successiveimages is below some desirable threshold).

As discussed above, act 310 may be performed at a plurality of viewangles to obtain projection data of the object at a number of desiredviews. For example, act 310 may be performed in accordance with any ofthe acquisition techniques described in the '848 patent and/or the '664application. In some embodiments, the object undergoing exposure is abreast or other radiation dose sensitive tissue, and one or both of theradiation intensity and/or radiation energy is varied as a function ofthe view angle (which may be distributed uniformly or non-uniformlyabout the object). In addition, acts 320 and 340 may be performedaccording to any of the reconstruction methods described in the '828,'848 patent and/or the parent application to obtain 3D images of theobject.

It should be appreciated that the second reconstruction may be performedon projection data that has already been obtained from the object. As aresult, image quality may be improved without requiring the object toundergo further radiation exposure, making it suitable for (though notlimited to) dose limited imaging procedures such as mammography.However, employing information obtained from one or more bootstrapimages to modify the projection data and/or to inform a secondreconstruction, may be used in generally dose insensitive environmentsas well, as the aspects of the invention are not limited in thisrespect.

FIG. 4 illustrates a method of obtaining information from an initialreconstruction to account for beam hardening effects, in accordance withsome embodiments of the present invention. Acts 410 and 420 may besimilar to the acts described in connection with FIG. 3. In particular,projection data may be obtained by exposing an object to radiation froma single or multiple view angles, and the projection data reconstructedto form a 2D or 3D bootstrap image of the density distribution, forexample, by using a relatively simple transmission model for theintensity-density relationship. In some embodiments, the projection datais obtained from a plurality of view angles and reconstructed to form a3D bootstrap image, according to any of the methods described inconnection with the 848' patent, or otherwise. In particular, theprojection data may be obtained in consideration of a relatively lowdose budget suitable for imaging sensitive tissue and/or performingroutine or frequent imaging procedures (e.g., breast imaging).

In act 430, an exit spectrum of the energy transmitted through theobject is estimated from information in the bootstrap image tofacilitate incorporating beam hardening effects into a subsequentreconstruction process. That is, the distribution of energy in theradiation exiting the object and impinging on the detectors isapproximated based on the bootstrap image. The estimated exit spectrumfacilitates performing a more accurate reconstruction that accounts fora polychromatic energy spectrum. In particular, the intensity-densityrelationship used to reconstruct a refined image (act 440) may accountfor the fact that 1) higher energy radiation results in proportionatelylarger detection signals 2) radiation at different energies may bedetected with different efficiencies, and 3) radiation at differentenergies have unique characteristic attenuation functions.

As discussed above, higher energy radiation is more transmissive thanlower energy radiation. As a result, more lower energy radiation istypically absorbed by the object than higher energy radiation.Therefore, the energy spectrum of the radiation penetrating the object,and more particularly, the proportion of lower energy radiation tohigher energy radiation will vary as a function of penetrationthickness. As the radiation penetrates more material, the more theenergy spectrum will be skewed in the direction of higher energyradiation due to the preferential absorption of lower energy radiation.Thus, the energy spectrum of the radiation may be substantiallydifferent at the detectors (exit spectrum) than it is at the radiationsource (emission spectrum).

As a general matter, detectors used in imaging procedures generate asignal proportional to the intensity of radiation detected at aradiation sensitive surface of the detector. However, the detectors maynot respond uniformly to radiation at every energy. In particular,higher energy radiation tends to produce larger detection signals forthe same intensity. Furthermore, radiation at different energies may bedetected with different efficiencies. Thus, a photon of relatively highenergy may produce a larger detector signal then a photon of relativelylow energy. However, when nothing is known about the energy spectrum,this energy-dependent response is typically ignored. That is, radiationof a given intensity is assumed to produce the same detection signalregardless of the radiation energy. The result is that the presence ofhigher energy radiation may produce detector signals that aredisproportionately large compared to the true intensity of impingingradiation.

To complicate matters further, the skew in the energy spectrum resultingfrom beam hardening results in a disproportionate (but generallyunknown) amount of higher energy radiation in the exit spectrum. Theresult is that, when the detection signals are interpreted without anyinformation about the energy spectrum, the recorded intensity of theradiation may be inaccurately low or inaccurately high, depending, atleast in part, on the density distribution of the object. In particular,when using a detector that creates a greater signal when higher energyphotons are detected, relatively high density material tends to beassigned lower densities values when polychromatic effects are ignored,resulting in reduced contrast images.

Since the simplified intensity-density model used to reconstruct thebootstrap image assumes monochromatic radiation, a particular intensityof radiation received at the detector may be assigned a particularmeaning with respect to the density of the object along the respectiveray during reconstruction. That is, the radiation along the respectiveray is assumed to have been uniformly attenuated according to a singleexponential attenuation function, rather than preferentially attenuatedaccording to multiple exponential attenuation functions that decay atdifferent rates depending on the radiation energy.

In particular, the characteristic attenuation function expressed inEquation 1 assumes energy independence. However, an attenuation functionthat more accurately expresses the physical process of radiationpenetrating matter can be expressed as,I(λ)=I ₀(λ)e ^(−ƒ(λ,μ)z)  (2).

As shown, the rate of attenuation is a function not only of thethickness z and the material specific absorption coefficient μ, but afunction of the energy λ of the radiation as well. However, if theenergy spectrum is unknown, some specific value of λ₀ must be selected(e.g., an estimated average energy) when performing reconstruction(e.g., the exit spectrum is assumed to be monochromatic radiation atsome energy λ₀). Accordingly, impinging radiation of energies differentthan λ₀ will be reconstructed according to an incorrect attenuationfunction. Thus, the monochromatic assumption may result in incorrectreconstruction of density values in conventionally reconstructed images.

By estimating the exit spectrum, the appropriate meaning may be assignedto radiation received at the detectors. In particular, the estimate ofwhat energies contributed to the detected radiation may allow thedetection signals to be properly interpreted, and further, may permitreconstruction of the projection data to be performed using theappropriate exponential attenuation function. For example, the exitspectrum indicates how much of the detected radiation intensity isattributable to different energy levels. Thus, the total detectedradiation intensity may be divided into sub-totals corresponding to theintensity attributable to the different energies in the spectrum. Thesub-totals may then be individually reconstructed to form correspondingdensity values for that energy, and the individual density values may becombined to form a single density based on a more accurate polychromaticmodel of the intensity-density relationship.

The exit spectrum may be computed based on an estimated emissionspectrum and the density values forming the bootstrap image. Inparticular, the energy spectrum emitted from the radiation source (i.e.,the emission spectrum) may be approximated based on knowledge of theradiation generation process and the properties of any filters usedbetween the radiation source and the object being exposed to theradiation. The density distribution represented by the bootstrap imagemay then be used to model the interactions of the penetrating radiationto estimate the effects on the emission spectrum, i.e., to approximatethe spectrum of the radiation exiting the object.

The emission spectrum may be approximated by taking into considerationproperties and characteristics of the imaging apparatus. As shown inFIG. 2, the energy spectrum emitted from a target at a given e-beamenergy is generally known. In some circumstances, a filter may bepositioned between the radiation source and the object to be exposed tofilter out certain energies. The passband of the filter (if present) incombination with the known characteristic spectrums of the targetmaterial and known e-beam energy may be used to compute an approximateemission spectrum. Any known or obtainable characteristics of theimaging apparatus may be used to estimate and/or assist in estimatingthe emission spectrum, as the aspects of the invention are not limitedin this respect.

By using the density distribution represented by the bootstrap image,the penetration effects on the emission spectrum may be approximated. Inparticular, the bootstrap image may be used to determine both thethickness of the object along the propagation paths associated with thevarious view angles, and the density distribution along those paths.This information may then be employed to compute the attenuation ofradiation at the various energies comprising the emission spectrum, forexample, according to the relationship shown in Equation 2. That is,since approximate density values (related in a known way to the μ valuesof matter within the object) and the thickness of the object along anydesired propagation path can be obtained from the bootstrap image, andthe initial intensity of radiation at the various energies are knownfrom the approximate emission spectrum, the attenuation of radiation ateach of the various energies may be computed to arrive at anapproximation of the exit spectrum.

In act 440, the approximate exit spectrum may be used to reconstruct theprojection data using a model that incorporates polychromatic effects.In particular, the exit spectrum may be used to determine whatproportion of the detected radiation intensity is attributable to thedifferent energies in the exit spectrum so that the detection signalscan be properly interpreted. For example, once the exit spectrum isknown, detector signals can be scaled up or down to more accuratelyreflect the actual intensity of the radiation at each of the variousenergies in the exit spectrum to account for the fact that higher energyradiation may result in larger detectors signals. In addition, eachdifferentiated intensity amount can be treated according to theappropriate attenuation function so that reconstruction is morereflective of the actual attenuation of the radiation at each of theenergies in spectrum. Accordingly, the second reconstruction may accountfor any number of polychromatic effects to improve the accuracy of thereconstruction and the quality of the resulting image.

In some embodiments, multiple exposures at different radiation energymay be obtained from the same view angle to estimate at least some beamhardening effects. As discussed above, matter tends to attenuate lowerenergy radiation more readily than higher energy radiation. By obtainingprojection data from the same view angle using different radiationenergy, the resulting projection data may be compared to estimate theamount of beam hardening that occurred. In particular, the projectiondata may be compared to characterize how the object is attenuatingradiation at different energy. This information may then be used toinform the reconstruction of the projection data to account for at leastsome beam hardening effects. One of the exposures at the same view anglemay be a low-dose exposure. The resulting projection data may be scaledbefore comparing the projection data with the one or more otherexposures performed at the same view angle. This allows the multipleexposures to be performed without significantly increasing the totaldose received by the object during the imaging procedure.

As discussed above, a bootstrap image may also be used to approximatethe amount of scattered radiation to correct the projection data and/orto inform a subsequent reconstruction of the projection data obtainedfrom exposing the object to radiation, to account for at least somescatter effects. In particular, the contribution of scattered radiationto detector signals produced from impinging radiation may be estimatedto assist in identifying portions of the detector signals resulting fromtransmitted radiation, such that a subsequent reconstruction avoidsincorrectly reconstructing information from scattered radiation as ifthe information was derived from transmitted radiation.

FIG. 5 illustrates a method of obtaining information from an initialreconstruction to account for scatter effects, in accordance with someembodiments of the present invention. Acts 510 and 520 may be similar tothe acts 310 and 320 described in connection with FIG. 3, and/or acts410 and 420 in connection with FIG. 4. In particular, projection datamay be obtained by exposing an object to radiation from a single ormultiple view angles, and the projection data reconstructed to form abootstrap image, for example, a 2D or 3D image from whichcharacteristics of the object (e.g., density characteristics, shapeinformation, size information, etc.) may be obtained.

In act 532, the information in the bootstrap image may be used toapproximate detector signal contribution resulting from scatteredradiation. As discussed above (e.g., in FIG. 1), radiation impinging onthe detectors may have arrived at the detectors either via transmission(i.e., substantially along a ray between the radiation source and thedetector) or via scattering (i.e., the radiation may have interactedwith atomic subject matter according to the Compton effect). However,since the simple transmission models assume that all radiation impingingon the detectors is transmitted, reconstruction may not account forscattered radiation. A significant portion (e.g., up to approximately50%) of detected radiation may be attributable scattered radiation. Inview of assumptions made during reconstruction, portions of projectiondata resulting from scattered radiation serve as noise manifesting inimage artifacts in the reconstructed image. Accordingly, an estimate ofthe scattered radiation may be used to correct the projection data suchthat resulting projection data is more reflective of purely transmittedradiation.

The amount of scattered radiation may be estimated by considering theshape of the object as represented in the bootstrap image. For example,FIGS. 6A and 6B illustrate embodiments for estimating scatter from abootstrap image (e.g., embodiments that may be performed in act 532). InFIG. 6A, image 600 a is a bootstrap image of an object 610. It should beappreciated that a real image of object 610 would include pixel valuescorresponding to the density distribution of and within the object. Forsimplicity of illustration, object 610 is shown as having a homogenousdensity distribution. In addition, images 600 a and 600 b areillustrated as 2D images, but may be, or be part of, 3D images as well(e.g., image 600 a may be a 2D slice of a 3D image).

As discussed above, as radiation passes through an object, someproportion of radiation is scattered by the atomic structure of theobject. Accordingly, each pixel (or voxel) in images 600 a and 600 b maybe viewed as a scatter center from which radiation could potentially bescattered. The bootstrap image, therefore, may facilitate generating amodel of the scatter by identifying where the density responsible forscatter is located. The probability that radiation will be scattered isa generally known or obtainable quantity. This probability increases asthe radiation reaches increased penetration depths because there is morematter that could potentially scatter the radiation (i.e., the radiationhas an increased likelihood of undergoing a Compton interaction withmatter the more matter the radiation has penetrated).

This principle can be used to generate a model of the scatter (e.g., togenerate an estimate of the contribution of scattered radiation on theprojection data). In some embodiments, the bootstrap image of the objectmay be divided into a plurality of segments, each at successive depthsof the object. For example, segments 605 a-605 l in FIG. 6A logicallydivide up image 600 at increased depths in a direction indicated byarrow 675, i.e., oriented generally away from radiation emitted by theradiation source. The contribution of scatter may be computed for eachsegment and then added together to estimate the total contribution ofscattered radiation.

For example, the amount of the matter in segment 605 a can be determinedfrom the bootstrap image (e.g., the number of pixels or voxels insegment 605 a may be counted to determine the number of scattercenters). The probability of radiation scattering at a depth dcorresponding to segment 605 a is generally known from the physics ofthe scatter phenomenon. Thus the number of scatter centers together withthe probability of scattering at each scatter center at a given depth dmay be used to approximate how much scatter radiation is generated insegment 605 a. This computation may be repeated for each of the segments605 and added together to approximate the amount of scatter resultingfrom radiation penetrating an object represented in the bootstrap image.

In some embodiments, the depths for which scatter is computed is basedon the distance of the scatter centers (e.g., pixel or voxel locations)along rays extending from a focal point as illustrated in FIG. 6B. Asdiscussed above, projection data may be obtained using a cone beam thatfans out from the focal point of the radiation source. Raysrepresentative of the propagation paths of radiation emitted duringexposure may be logically superimposed on the bootstrap image and thepenetration depth may be based on the distance along the respective raysfrom a location at which the ray first penetrated the object. By usingrays indicative of the propagation paths of radiation used duringexposures to obtain the projection data, a more accurate measure ofpenetration depth may be obtained. It should be appreciated that anestimate of radiation scatter based on the location of scatter centersidentified in the bootstrap image may be obtained in other ways, as theaspects of the invention are not limited in this respect.

In act 534, the projection data may be modified in view of the estimatedcontributions of scattered radiation obtained from the bootstrap image.In particular, the effects of scattered radiation may be removed fromthe projection data such that the projection data is more representativeof transmission effects only. That is, when the estimated detectorsignal contributions due to scattered radiation have been removed fromthe projection data, the projection data may more accurately reflectassumptions made during reconstruction (i.e., that the projection dataarose from transmitted radiation). The modified projection data may thenbe reconstructed to form an image of the object that more correctlyrepresents the density distribution of the object (act 540).

In some embodiments, multiple exposures at different radiation energymay be obtained from the same view angle to estimate scatteredradiation. Radiation at different energy tends to be scattered bydifferent amounts. By obtaining projection data from the same view angleusing different radiation energy, the resulting projection data may becompared to estimate scattered radiation. The differences in theprojection data obtained at different radiation energies will bepartially attributable to the differences in how radiation at differentenergies is scattered. The estimate of the scattered radiation may thenbe used to modify the projection data to remove at least some of thecontribution attributable to scattered radiation. The modifiedprojection data may then be reconstructed to form one or more images.One of the exposures at the same view angle may be a low-dose exposure.The resulting projection data may be scaled before comparing theprojection data with the one or more other exposures performed at thesame view angle. This allows the multiple exposures to be performedwithout significantly increasing the total dose received by the objectduring the imaging procedure.

It should be appreciated that the techniques of incorporatingpolychromatic effects and scatter effects may be combined to furtherimprove subsequent reconstructions. For example, information obtainedfrom one or more bootstrap images to differentiate intensitycontributions from transmitted radiation and scattered radiation, and toestimate and compensate for polychromatic effects may be used togetherto perform a reconstruction that more accurately reflects the actualdensity distribution of the object being imaged. In addition, thevarious methods of employing information from one or more bootstrapimages to inform a subsequent reconstruction, can be used alone or incombination with other techniques for accounting for various penetrationeffects, as discussed in further detail below.

As discussed above, absent a priori knowledge, it may not be possible todifferentiate contribution to detector signals from transmittedradiation and from scattered radiation. The foregoing describes, amongstother things, techniques for obtaining estimates of scattered radiationfrom one or more bootstrap images to remove at least some of the scattereffects in the resulting images. Anti-scatter grids yield anotherpotential method for estimating scatter effects, in accordance withembodiments of the present invention. Conventionally, anti-scatter gridshave been used to block scattered radiation from impinging on a detectorarray to ensure that substantially all of the impinging radiation at thedetector array is transmitted radiation. However, conventional use ofanti-scatter grids does not provide an estimate of scatter, but insteadmerely prevents scattered radiation from ever contributing to theprojection data.

FIG. 7 illustrates concepts related to using an anti-scatter grid toprevent scattered radiation from impinging on a detector array. In FIG.7, a radiation source 720 is arranged to provide radiation to anexposure area 716 where an object 710 may be positioned for exposure tothe radiation. The radiation source 720 may provide, for example, a conebeam of radiation to the exposure area. A detector array 730 may bepositioned beyond the exposure area to detect at least some of theradiation that penetrates and exits object 710 to obtain projection dataof the object. An anti-scatter grid 770 may be positioned in front ofthe detector array to block radiation that is not propagating in adirection characteristic of transmitted radiation. In particular,anti-scatter grid 770 comprises a plurality of slots formed by a grid ofdividers made from material of relatively high density (e.g., lead)adapted to absorb all or substantially all of the radiation impinging onthe surface of the dividers (e.g., exemplary slots 771 and dividers772). The dividers are angled in such a way that the propagation pathsinto the slots converge at the focal point of radiation source 720.

A number of exemplary rays, indicating possible radiation propagationpaths, are shown to illustrate the function of the anti-scatter grid.The rays illustrate possible propagation paths in which radiation (e.g.,photons) may travel from the radiation source through the exposure area.Rays 722 indicate exemplary propagation paths of transmitted radiation,i.e., radiation that does not interact with the atomic structure ofobject 710. The dividers 772 are angled such that radiation emitted fromthe focal point of radiation source 720 and passing unaffected throughobject 710 can impinge on the detector array via the slots 771.

Rays 724 illustrate potential propagation paths for scattered radiation,e.g., radiation that interacts with the atomic structure of object 710according to the Compton effect. Due to the fact that scatteredradiation is emitted from a source point (i.e., the atom from which itinteracted) different than the focal point of the radiation source, thescattered radiation is unlikely to propagate in a direction that avoidsimpinging on one of the dividers. For example, radiation propagatingalong ray 724 a undergoes a Compton interaction with an atom 711. As aresult, radiation is emitted along ray 726 a. Because the radiation hasa different propagation path that does not converge with the focalpoint, the radiation along ray 726 a will be absorbed by one of thedividers and prevented from impinging on the detector. Various otherscattered propagation paths (e.g., paths 726 b, 726 c and 726 c) areshown to illustrate how the anti-scatter grid prevents scatteredradiation from impinging on the detector array and contributing to thedetector signals forming projection data obtained from object 710.

Anti-scatter grids have been used conventionally to obtain projectiondata that is substantially free of the effects of scattered radiation.This projection data is then reconstructed to form an image of thestructure of an exposed object. However, certain imaging geometries maybe incapable of using an anti-scatter grid at multiple view angles. Forexample, some imaging equipment is designed to obtain projection datafrom a plurality of view angles by moving the radiation source about theobject while leaving the detector or detector array stationary. As aresult, an anti-scatter grid may be useable only at the single viewangle where the slots are aligned with the focal point of the radiationsource. In particular, an anti-scatter grid is typically designed tooperate correctly only at a particular alignment with the radiationsource. Accordingly, if the detector array and anti-scatter grid are notmoved in correspondence, the anti-scatter grid may be thrown out ofalignment such that even transmitted radiation will not reach thedetectors. Accordingly, certain imaging equipment configurations may beunable to use anti-scatter grids at multiple view angles.

Applicant has appreciated that estimates of scatter obtained usinginformation provided by an anti-scatter grid may be used both to modifyprojection data obtained at the view angle wherein the anti-scatter gridwas used, and to modify projection data obtained from one or more otherview angles where no anti-scatter grid was used and/or where noanti-scatter grid was available. Thus, imaging equipment, for example,wherein the radiation source and detector array do not move incorrespondence may still benefit from scatter estimates obtained usingan anti-scatter grid.

FIG. 8 illustrates a method of reducing the effects of scatter using ananti-scatter grid, in accordance with one embodiment of the presentinvention. In act 810, an object is exposed to radiation and firstprojection data is obtained. This first exposure may be performedwithout an anti-scatter grid, generally at the full dose that isappropriate for obtaining projection data of the object. For example, adose budget may be set at an appropriate level for obtaining projectiondata from multiple view angles, and the dose for the first exposure maybe an appropriate percentage of the total dose budget. Since theobtained projection data is intended for reconstruction to form one ormore images (referred to as reconstruction projection data), thereconstruction projection data may be obtained at exposure levelssufficient to provide a desired resolution and contrast. As discussedabove, the projection data obtained in this manner will includecontributions from both transmitted and scattered radiation.

In act 820, a second exposure is performed at the same view angle usingan anti-scatter grid to obtain anti-scatter projection data. The secondexposure may be performed at a lower dose than the first exposure. Theprimary purpose of the anti-scatter projection data is to approximatethe contribution of scattered radiation in detection signals produced inresponse to the first exposure and, more particularly, to compute therelative proportion of transmitted radiation to scattered radiation.Accordingly, the second exposure may be performed at a substantiallylower dose because high resolution information (e.g., high contrastinformation) may not be required from the anti-scatter projection data.As a result, the second exposure may be performed without spending muchof the intended total dose budget. For example, in breast imaging, thetotal subject dose received by the patient may be limited for safetypurposes. Accordingly, by obtaining anti-scatter projection data atlower exposure levels, more of the dose budget is preserved forobtaining projection data that will ultimately be reconstructed to formimages (e.g., diagnostic images of the breast).

In act 830, the reconstruction projection data obtained from the firstexposure is modified based on the anti-scatter projection data obtainedfrom the second exposure. In some embodiments, the difference betweenthe anti-scatter projection data and the reconstruction projection datais computed. By subtracting the anti-scatter projection data fromreconstruction projection data, the contribution of transmittedradiation is subtracted out, leaving substantially only the contributionof the scattered radiation. This difference (i.e., the estimate of thescatter effect) may then be subtracted from the reconstructionprojection data to remove at least some of the contribution of thescattered radiation from the reconstruction projection data.

In embodiments where the first and second exposures are performed usingdifferent radiation doses, one or both of the reconstruction projectiondata and the anti-scatter projection data may need to be scaled to placethe intensity values in the same range to permit appropriate comparison.For example, when the first exposure is performed at intensity and/orenergy levels appropriate for obtaining relatively high contrastprojection data (e.g., contrast suitable for producing diagnosticquality images), and the second exposure is performed using a reduced orsubstantially reduced dose, one or both of the projection data obtainedmay need to be scaled to ensure that any comparisons (e.g., differences)or modifications to the projection data is performed on data at the samescale.

In particular, if the anti-scatter projection data is obtained usingemission intensities lower than those used to obtain the reconstructionprojection data, the intensity of impinging radiation will naturally belower as a consequence. As a result, the contributions of scatteredradiation to the anti-scatter projection data will not be reflective ofthe contributions of scattered radiation to the reconstructionprojection data, though the ratios may be similar. Accordingly, theanti-scatter projection data may be scaled up, or the reconstructionprojection data may be scaled down to facilitate meaningful comparisonsbetween the two sets of projection data. It should be appreciated thatin embodiments where exposure levels are the same or similar for bothexposures, scaling may be unnecessary.

In act 840, the modified projection data is reconstructed to form animage of the density distribution of the object which has been correctedfor scatter effects. As a result, the image is reconstructed fromprojection data wherein contributions from scattered radiation have beenreduced or eliminated. It should be appreciated that the exposures withand without the anti-scatter grid may be performed in either order, andthe embodiment described above wherein the projection data without theanti-scatter grid is obtained first is merely exemplary, as the aspectsof the invention may be used with projection data obtained in any order.

As discussed above, and described in the '848 patent, it may beadvantageous to obtain projection data of an object from multiple viewangles so that a 3D image of the object may be reconstructed. The '848patent describes methods and apparatus for obtaining projection datafrom multiple view angles in a relatively low-dose environment such asimaging procedures involving human tissue and/or procedures that areperformed regularly (e.g., low-dose environments suitable for breastimaging). The method of using projection data obtained with ananti-scatter grid to correct projection data obtained without ananti-scatter grid may be particularly suitable for such environments.Applicant has appreciated that estimates of radiation scatter obtainedat one or more view angles may be used to approximate radiation scatterat other view angles at which actual exposures to collect scatterinformation are not performed, thus preserving more of the dose budgetfor exposures where relatively high resolution information may beneeded.

FIG. 9 illustrates one method of compensating for scatter effects inprojection data obtained from a plurality of view angles, in accordancewith one embodiment of the present invention. In act 910, anti-scatterprojection data is obtained at a first view angle. In particular, ananti-scatter grid may be placed between the object and the detectorarray to absorb radiation scattered by the object. In some embodiments,the anti-scatter projection data is obtained using a lower dose thanused to obtain subsequent first projection data to preserve the dosebudget for exposures where resulting projection data is intended to bereconstructed to form image data. Since the anti-scatter projection datais obtained to correct for scatter effects in the higher dose projectiondata, it may be obtained under relatively low-does conditions withrespect to exposures obtained for the purposes of image reconstruction.However, the reconstruction and anti-scatter projection data may beobtained at the same or similar exposure levels.

In act 920, first reconstruction projection data of an object isobtained at the first view angle without using an anti-scatter grid. Inone embodiment, the first projection data is obtained at the fullexposure allocated to each view angle in consideration of a particulardose budget (e.g., a dose budget suitable for safely performingmammography). Since the first reconstruction projection data willultimately be reconstructed to form, at least in part, a 3D image, theprojection data should be obtained at a relatively high resolution suchthat reconstructed images have the contrast necessary to properlydistinguish the internal structure of the object (e.g., in breastimaging, the contrast should be high enough to accurately differentiatebetween healthy and anomalous breast tissue).

In act 930, next reconstruction projection data is obtained at a nextview angle. Like the first reconstruction projection data, the nextreconstruction projection data may be obtained at the full doseallocated for each view angle according to a given dose budget. In act935, it is determined whether anti-scatter projection data should beobtained at the next view angle. As discussed above, anti-scatterprojection data need not be obtained at each view angle thatreconstruction projection data is obtained. In particular, anti-scatterprojection data obtained from one or more view angles may be used toapproximate scatter at other view angles, as discussed in further detailbelow. By estimating anti-scatter projection data, rather than obtainingthe anti-scatter projection data via an additional exposure, preservesmore of the dose budget for reconstruction projection data where highresolution/high contrast acquisition may be more important, and the dosebudget more appropriately spent.

Depending on the determination made in act 935, either anti-scatterprojection data is obtained at the next view angle (act 940), or adetermination is made as to whether reconstruction projection datashould be obtained at further view angles (act 945). If furtherreconstruction projection data is desired, the appropriate actsbeginning at act 930 may be repeated. It should be appreciated that actsinvolved in performing exposures may be repeated any number of times toobtain reconstruction projection data and anti-scatter projection dataat any desired view angles, respectively.

In some embodiments, the view angles at which reconstruction projectiondata is obtained form a range, and anti-scatter projection is obtainedat least at the extremes and at the midpoint of the range, and otherwiseinterpolated, as described in further detail below. However, it shouldbe appreciated that anti-scatter projection data may be obtained at anynumber and arrangement of view angles, as the aspects of the inventionare not limited in this respect.

In some embodiments, anti-scatter projection data is obtained from asingle view angle. The anti-scatter projection data may then be used toestimate the scatter at other view angle from which no anti-scatterprojection data is obtained. For example, in imaging equipment that doesnot move the radiation source and radiation detector or detector arrayin correspondence when obtaining projection data from different viewangles, an anti-scatter grid may be useful from only the single viewangle for which it was adapted. Accordingly, anti-scatter projectiondata obtained from the view angle for which is was constructed may beobtained and subsequently employed to estimate the scatter at other viewangles. It should be appreciated that anti-scatter projection dataobtained from one view angle may be used to estimate scatter at anotherview angle even in the event that anti-scatter projection data couldhave been obtained from any of the view angles, as discussed in furtherdetail below.

In act 950, an estimate of the scatter at the first view angle isobtained. For example, the scaled or unscaled difference between thefirst reconstruction projection data obtained at the first view angleand the anti-scatter projection data obtained at the first view anglemay be used as an estimate of the scatter at the first view angle.However, an estimate of the scatter based on the projection dataobtained with and without the anti-scatter grid may be computed in otherways, as the aspects of the invention are not limited in this respect.

In act 960, an estimate of the scatter at the next view angle whereprojection data was obtained (in the event that anti-scatter projectiondata was obtained for multiple view angles) both with and without ananti-scatter grid is computed. As discussed above, the estimate of thescatter may be performed by any suitable comparison between thereconstruction projection data and the anti-scatter projection data thatprovides a useful estimate of the scatter. Act 960 may be repeated foreach view angle where both reconstruction projection data andanti-scatter projection data was obtained.

In act 970, the determined estimates of scatter from the one or moreview angles are used to modify the reconstruction projection data toremove at least some of the effects of scattered radiation. For example,in the first instance, the estimate of the scatter at the first viewangle may be subtracted from the first reconstruction projection data toremove at least some of the scatter effects. In act 975, it isdetermined whether an estimate of the scatter is available at the nextview angle. In particular, since anti-scatter projection data may nothave been obtained via an exposure at each of the plurality of viewangles, some of the reconstruction projection data may not have acorresponding estimate of the scatter at the associated view angle.

If it is determined that an estimate of the scatter at a current viewangle under consideration is present, then the reconstruction projectiondata is modified according to the corresponding estimate of the scatter(i.e., act 970 may be performed at the current view angle, and the nextview angle may be assessed in act 975). If it is determined that noestimate of the scatter is available at the current view angle, then anestimate of the scatter at the current view angle may be determined fromanti-scatter projection data and/or estimates of the scatter availableat one or more other view angles (act 980).

In act 980, an estimate of the scatter at the current view angle isobtained from scatter information obtained at one or more other viewangles where anti-scatter projection data was obtained via exposure. Forexample, the estimate of the scatter computed at the nearest lesser viewangle and the nearest greater view angle may be used to estimate thescatter at the current view angle. In some embodiments, the estimate ofthe scatter at the current view angle is obtained by interpolating theestimate of the scatter from the nearest lesser and greater view angles.Alternatively, the estimate of the scatter may be obtained by using theanti-scatter projection data obtained at any of the view angles (e.g.,the first view angle) for which an anti-scatter grid was used, as theaspects of the invention are not limited in this respect.

Once an estimate of the scatter is obtained, the estimate may be used tomodify the reconstruction data at the current view angle to remove atleast some of the effects of scattered radiation from the reconstructionprojection data (e.g., act 970 may be performed on the currentreconstruction projection data and the computed estimate of the scatterat the current view angle). It should be appreciated that anti-scatterprojection data obtained via exposure may be used to form estimates ofscatter at view angles where no anti-scatter projection data wasobtained in other ways, as the aspects of the invention are not limitedin this respect. The acts of correcting reconstruction view data basedon estimates of the scatter (either obtained via exposure or computedfrom estimates obtained via exposure) may be repeated for each of theview angles at which reconstruction projection data was obtained.

In some embodiments, anti-scatter projection data is obtained from asingle view angle and used to estimate scatter at the view angle fromwhich it was obtained and each other view angle where reconstructionprojection data was obtained. In some embodiments, a first exposure isperformed from a reference view angle at a relatively high dose, and anumber of subsequent exposures are obtained at slight rotations in viewangle from the reference view angle and lower doses (e.g., as describedin the '848 patent). Anti-scatter projection data may be performed atthe reference view angle and used to estimate the scatter at the otherview angles.

In act 990, the reconstruction projection data modified by the estimatesof scatter may be reconstructed to form an image of the object, forexample, a 3D image of the object. Because the projection data has hadat least a portion of the scatter effects removed, the resulting imagemay more accurately reflect the actual density distribution of theobject.

As discussed above, without any a priori information, it may bedifficult to differentiate different contributions to the detectorsignals resulting from impinging radiation (e.g., contributions fromtransmitted radiation, scattered radiation, polychromatic radiation,etc.), which are often modeled as a single contribution (e.g., detectorsignals may be assumed to have resulted only from monochromatictransmitted radiation). Applicant has appreciated that using densityfiducials during exposure of an object may provide information that maybe used to facilitate differentiating contributions from one or morepenetration effects, and/or otherwise providing information in abootstrap image that may be employed to modify the projection dataand/or inform a subsequent reconstruction.

The term “density fiducial” refers herein to material of generally knowndensity positioned within an exposure area along with an object to beexposed such that at least some of some radiation passing through theexposure area impinges on the density fiducial. The term fiducial isused to indicate that typically the density and/or location of thefiducial is generally known a priori. A density fiducial positionedbetween a radiation source and the object is referred to as a proximaldensity fiducial (or located proximally) and a density fiducialpositioned between the object and a detector array is referred to as adistal density fiducial (or located distally). A density fiducial may beof any desired density, shape or size, as the aspects of the inventionare not limited in this respect.

In some embodiments, partially transmissive density fiducials (e.g.,density fiducials that partially absorb and partially pass impingingradiation) are used to obtain information that can be used to modifyprojection data and/or facilitate more accurate reconstruction. Inparticular, by placing density fiducials of known density in knownlocations, a priori information is made available to the reconstruction.Partially transmissive density fiducials may be used, amongst otherthings, to both estimate scatter, to assist in calibrating detectorsignals, and to assist the reconstruction by providing a volume of knowndensity, as discussed in further detail below.

FIG. 10 illustrates concepts related to using partially transmissivedensity fiducials to obtain an estimate of scattered radiation, inaccordance with some embodiments of the present invention. In FIG. 10, afirst partially transmissive density fiducial 1080 a is positionedproximally with respect to the object. That is, proximal fiducial 1080 ais positioned between a radiation source (not shown) and the object 1010being imaged. For simplicity of illustration, the radiation isillustrated as propagating along a plurality of parallel rays. However,it should be appreciated that non-parallel rays (e.g., the propagationpaths of radiation emitted in a cone-beam) may be used as well, as theaspects of the invention are not limited in this respect. In particular,the concepts described in connection with FIG. 10 may apply to radiationfields of any shape and/or configuration. A second partiallytransmissive density fiducial 1080 b may be positioned distally, suchthat at least some radiation penetrating through object 1010 interactswith density fiducial 1080 b.

In the embodiment illustrated in FIG. 10, the density of the proximaland distal fiducials are chosen such that approximately 50% of radiationimpinging on the fiducial will be transmitted and 50% will be absorbed.However, the density selected is merely exemplary and was chosen to bestillustrate concepts related to using generally matched density fiducialsto estimate scatter. Since density fiducial 1080 a is placed proximally,the intensity reduction resulting from the fiducial is applied only toprimary radiation (i.e., non-scattered radiation) because no substantialsubject matter interacts with the radiation to cause scattering prior toimpinging on density fiducial 1080 a. To illustrate the principle,object 1010 is shown as absorbing about 50% of the radiation through thethickness underneath density fiducial 1080 a. Accordingly, approximately25% of the radiation impinging on proximal density fiducial 1080 a istransmitted through the object to impinge on the detectors in the shadowof the fiducial.

Since density fiducial 1080 b is placed distally, the intensityreduction resulting from the fiducial will be applied to all of theradiation impinging on the fiducial; both transmitted and scattered. Asa result, the intensity reduction from the perspective of the detectorsin the shadow of density fiducial 1080 b will be more significant thanthe intensity reduction from the perspective of the detectors in theshadow of density fiducial 1080 a. Accordingly, the difference betweenthe intensity reduction from the respective density fiducials may beused to estimate the scatter.

For example, there is substantially the same amount of radiationabsorbing subject matter between the radiation source and the detectorsin the shadow of the respective density fiducials (i.e., the detectorsin region 1030 a and region 1030 b, respectively). In particular, thereare the density fiducials themselves (which may be identical orsubstantially identical is shape, size and/or density to each other) andsubstantially the same thickness of object 1010. In addition,substantially the same amount of scatter radiation will converge in thearea directly above regions 1030 a and 1030 b. However, the detectors inregion 1030 a will record a greater intensity than the detectors inregion 1030 b due to the positioning of the density fiducials.

In particular, substantially all of the scattered radiation present inthe object immediately above region 1030 a will directly impinge on thedetectors, while a substantially equal amount of scatter radiationpresent in the object immediately above region 1030 b will be attenuatedby density fiducial 1080 b. Thus, detectors in region 1030 b will recordless intensity in an amount related to the absorption ratio of thedensity fiducials. As discussed above, this difference is related toamount of scattered radiation as illustrated in FIG. 10, and may be usedto provide a scatter estimate that may be employed to modify theprojection data to account for at least some scatter effects.

It should be appreciated that FIG. 10 is schematic and not drawn toscale. The relative size of the density fiducials with respect to theobject was chosen to illustrate the concept of using proximally anddistally positioned density fiducials to estimate scatter, and may notbe indicative of actual relative sizes. In addition, the absorptioncharacteristics of the density fiducials was selected to highlight thedifferential in intensity reduction. However, density fiducials of anydensity may be used, as discussed in further detail below.

In some embodiments, the object being imaged is a human female breastand the density fiducials are a part of or affixed to the compressionmechanism that positions and compresses the breast in preparation forimaging. For example, FIG. 11 illustrates a schematic diagram of abreast 1110. The breast is held in place and compressed by compressionpaddles 1130 a and 1130 b. Density fiducials 1180 a and 1180 b areimplemented as portions of the compression paddles. In otherembodiments, the density fiducials are affixed to the compressionpaddles so that they are removable, allowing density fiducials of anydesired density to be positioned within an exposure area and employed toestimate scatter and/or calibrate detector signals. In still otherembodiments, the density fiducials are affixed to the object itself. Instill other embodiments, distal density fiducials are affixed to aportion of the detector array. It should be appreciated that densityfiducials may be positioned and/or affixed proximally and distally inany manner, as the aspects of the invention are not limited in thisrespect.

FIG. 12 illustrates a method of obtaining an estimate of radiationscatter by employing density fiducials, in accordance with someembodiments of the present invention. In act 1210, density fiducials maybe positioned with respect to an object being imaged. In someembodiments, a proximal density fiducial is positioned between theobject and a radiation source adapted to provide radiation to theobject. The proximal density fiducial may be partially transmissive toabsorb some desired proportion of radiation penetrating the fiducial. Inaddition, a distal density fiducial may be positioned between the objectand a detector array adapted to detect radiation exiting the object. Theproximal and distal density fiducials may be selected to havesubstantially the same density, such that they absorb substantially thesame proportion of penetrating radiation.

In act 1220, the object is exposed to radiation to obtain projectiondata of the object. Multiple exposures may be performed to obtainprojection data from a plurality of view angles, distributed uniformlyor non-uniformly about the object. In act 1230, the amount of scatteredradiation is estimated from the projection data. In particular, theprojection data obtained from one or more view angles may be analyzed inconnection with the density fiducials to estimate the data. For example,the detector signals from detectors in the shadow of the proximal anddistal fiducials from at least one view angle may be compared. Asdiscussed above, discrepancies in the intensity recorded in the shadowof matched pairs of proximal and distal fiducials may be used toindicate the amount of scattered radiation produced by the object.

In act 1240, the projection data is modified to account for the scatter.For example, the contribution to the recorded intensities at thedetector array from the estimated scatter may be subtracted from theprojection data to remove at least some of the effects of scatteredradiation. The modified projection data may then be reconstructed toform an image of the object (act 1250), for example, a 3D image may beobtained from reconstructing the projection data acquired from theplurality of view angles. Therefore, at least some of the imageartifacts resulting from scattered radiation may be removed.

In some embodiments, the proximal and distal density fiducials may beaffixed directly to the object being imaged. For example, the densityfiducials may be an adhesive of a desired density applied directly tothe object. In some embodiments, the distal density fiducial is affixedto the detector array. In some embodiments, the object being imaged is ahuman female breast and a compression mechanism is used to compress thebreast and hold the breast in place during the imaging procedure. Insuch embodiments, the density fiducials may be affixed to and/or be apart of the compression mechanism. As discussed above, the densityfiducials may be of any shape, size or density, as the aspects of theinvention are not limited in this respect. In some embodiments, thedensity fiducials are approximately 1 mm²-3 mm² in area.

In some embodiments, the density fiducials have a density which is inthe range between 75% and 150% percent of the density of the predominantdensity in the object being imaged. In particular, in some imagingprocedures, the object being imaged may have a characteristic densityand/or may be of a generally homogeneous density, and the density of thefiducials may be selected in view of the characteristic and/orhomogeneous density. For example, in mammography, the female humanbreast is made primarily of fatty tissue, which itself is composedsignificantly of water. Accordingly, the breast may have acharacteristic density of typical breast tissue and the densityfiducials may be selected to have some predetermined percentage of thatdensity. In some embodiments, the density fiducials have a densitygreater than 150% of the characteristic density of the object beingimaged. It should be appreciated that density fiducials of any densitymay be chosen, as the aspects of the invention are not limited in thisrespect.

As discussed above, partially transmissive density fiducials may beemployed to facilitate calibrating the intensity of radiation impingingon the detectors. Reconstructing an image from projection data involvesdetermining the relationship between recorded intensity and the densityof the object. Stated differently, image reconstruction may involvemapping recorded intensities to density values. The appropriate mappingmay be assisted by placing partially transmissive fiducials of knowndensity within the exposure area. For example, by having subject matterof known density and known location in the exposure area, the recordedintensities at detectors associated with those locations can be assignedthe known density values, and other intensity may be mapped accordinglyrelative to the known mapping at the density fiducials.

It should be appreciated that the intensity to density mapping may notbe linear. That is, an increment in recorded intensity may not map to acorresponding increment in density due in part to the exponentialattenuation function, beam hardening, scatter etc. Accordingly, themapping between recorded intensity and density may be some function. Theknown density values and locations of partially transmissive fiducials,therefore, may be used to determine the slope of the curve that mapsrecorded intensity values to density values.

In some embodiments, the different intensity reductions caused byproximal and distal density fiducials respectively may be used toestimate beam hardening effects. In particular, if the proximal anddistal density fiducials are of the same thickness and are made of thesame material, differences in the apparent transmissivity (e.g., asindicated by the recorded intensities) may be due in part to beamhardening. Specifically, because the lower energy radiation ispreferentially absorbed, a greater proportion of higher energy radiationwill impinge on the distal density fiducial than will impinge on theproximal density fiducial, making the distal density fiducial appearmore transmissive. Accordingly, discrepancy between the apparenttransmissiveness of the matched density fiducials may be used toapproximate the effects of beam hardening.

As an alternative to, or in combination with, partially transmissivedensity fiducials, one or more density fiducials that are more or lessopaque to radiation may be used to gain information that may be used tocorrect projection data and/or otherwise inform reconstruction about oneor more effects not accounted for by the simplified model. FIG. 13illustrates how an opaque density fiducial may be used to estimate theamount of scattered radiation.

In FIG. 13, a radiation source 1320 is arranged to expose an object 1310to radiation, and a detector array 1330 is positioned to detectradiation penetrating and exiting the object to collect projection data.Some amount of the radiation emitted by radiation source will betransmitted (e.g., exemplary ray 1322 a) to impinge on the detectorarray, some amount will be absorbed according to the photoelectriceffect (e.g., exemplary ray 1324 a), and some amount will be scatteredaccording to the Compton effect (e.g., exemplary ray 1326 a). However,as discussed above, the transmitted radiation and the scatteredradiation impinging on the detector array are generallyindistinguishable. As a result, reconstructions that assume detectorsignals were produced by transmitted radiation alone will suffer fromimage artifacts associated with incorrectly interpreted detector signalsresulting from scattered radiation.

An opaque density fiducial 1375 positioned proximally will absorbradiation impinging on its surface, casting a shadow on the detectorarray (i.e., on detectors in portion 1330 a) wherein no transmittedradiation will impinge. As a result, any radiation detected at portion1330 a can be attributed to scattered radiation. For example, someamount of radiation will be scattered by object 1310 and will impingewithin the shadow of the density fiducial (e.g., exemplary scatteredrays 1326 b-1326 e).

The detected radiation may be used to approximate the contribution ofscattered radiation on the detector signals. That is, the detectorsignals generated in region 1330 a may be used as a measure of theamount of radiation being scattered by object 1310. The estimate of thescattered radiation may be used to adjust the detector signals toaccount in part for scatter in the reconstruction of the projection dataobtained by exposing object 1310 to radiation from a plurality of viewangles. In particular, the detector signal generated by detectors in theshadow of opaque density fiducial 1375 may be used as an estimate of thehow much scattered radiation is contributing to the detector signals atdetectors that are not in the shadow of the density fiducial.Accordingly, the projection data may be modified to remove contributionsestimated as being attributable to scattered radiation. An imagereconstructed from the modified projection data, therefore, will havebeen compensated, to some extent, for scatter effects.

Applicant has identified further methods in which a bootstrap image maybe used to inform reconstruction of projection data to reduce and/oreliminate image artifacts, errors or otherwise improve the quality ofthe resulting image. Applicant has recognized that in conventionalreconstruction, due generally to the absence of a priori informationabout the boundary of the object being imaged, locations outside of theobject may be assigned non-zero density values. That is, some of theattenuation contribution will be attributed to surrounding matter suchas air. Assigning density values to surrounding matter that contributednegligibly or did not contribute at all to the attenuation of radiationresults in assigning incorrect density values to matter within theboundaries of the object.

As will be appreciated by those skilled in the art, image reconstructionfrom limited projections is generally ill-posed (i.e., there are moreunknowns than knowns) such that the reconstruction algorithm operatingon given projection data will not have a single unique solution.Accordingly, a reconstruction algorithm, for example, an iterativealgorithm such as a gradient descent approach, may converge to a localminimum. Accordingly, the more constraints the algorithm has, the lesslikely the algorithm will be to converge to a local minimum havingrelatively significant errors in the distribution of density values.

When intensity is incorrectly assigned outside the boundary of anobject, the intensity assigned within the boundary of the object will beincorrectly assigned, approximately to the same extent, resulting inartifacts in the resulting images. Applicant has appreciated thatinformation about the object boundary can be used to constrain thereconstruction to produce an image that is more reflective of the actualdensity distribution of the object. Artifacts associated withincorrectly assigning intensity values outside the boundary of an objecttend to effect the intensity values near the boundary more thanintensity levels further away from the boundary. This effect may beparticularly deleterious for mammography images where anomalous tissuemay be located near the surface of the breast.

In some embodiments, a bootstrap image is reconstructed from projectiondata obtained by exposing an object to radiation. The bootstrap image isprocessed to identify a boundary of the object. The identified boundaryis used to constrain a second reconstruction of the projection data toform an image representing a density distribution more reflective of thedensity distribution of the object. In some embodiments, one or moredensity fiducials are arranged in contact with or proximate to an objectto be imaged to define the boundary of the object. A bootstrap image maybe reconstructed from projection data obtained during one or moreexposures of the object in the presence of the one or more densityfiducials. The density fiducials may be identified in the bootstrapimage to locate the boundary of the object, and the located boundaryused to constrain a second reconstruction of the projection data.Alternatively, recognizable features of the object that are located atthe object boundaries can be used to identify the object boundaries. Forexample, in a breast image, the pattern of the skin may have adetectable property that is recognizable from that of the interiorbreast tissue.

FIG. 14 illustrates a method of using boundary information to constraina reconstruction of projection data, in accordance with variousembodiments of the present invention. In act 1410, one or more densityfiducials are positioned in contact or proximate the boundary of anobject to be exposed to radiation. Preferably, one or more of thedensity fiducials are placed in contact with the object to demarcate theboundary. The one or more density fiducials may be made of a materialhaving a density that is salient with respect to the object such that itis relatively easy to identify in an image. For example, the one or moredensity fiducials may be partially transmissive or partially opaque toradiation emitted by a radiation source during an exposure. As a result,the one or more density fiducials may be relatively easy to locate in areconstructed image, for example, using any of various automatic imageprocessing algorithms.

In some embodiments, a plurality of density fiducials are spaced apartas to not block substantial amounts of radiation. The plurality ofspaced apart density fiducials may be used to identify portions of theboundary of the object. The boundary of the object between the densityfiducials may be interpolated and/or otherwise determined based ongeneral knowledge about the shape of the object. For example, in breastimaging, the breast shape is generally known (e.g., the breast, whencompressed, is generally elliptical and has a generally continuous andsmoothly transitioning boundary) and gaps in the boundary betweendensity fiducials may be approximated, interpolated or otherwisedetermined based on this knowledge. For example, one or more curves maybe fit between the density fiducials to approximate the boundary.

In addition, other image processing techniques may be used to determinethe boundary between the density fiducials such as edge detection and/orthe detection of other morphological characteristics of the boundary ofthe object, as discussed in further detail below. It should beappreciated that density fiducials (when opaque) prevent radiation frombeing transmitted through the breast underneath the shadow of thedensity fiducial. Accordingly, it may be beneficial to place the densityfiducials strategically. For example, in breast imaging, it may bebeneficial to place the density fiducials at boundary locations ofhigher curvature where it may be more difficult to interpolate betweendensity fiducials.

While opaque density fiducials block radiation that may otherwise carryinformation about the structure of the object, it should be appreciatedthat in imaging procedures where projection data is obtained from aplurality of view angles, the density fiducials will cast a shadow ondifferent portions of the object at each view angle. Accordingly, thedifferent views may be used to ensure that sufficient information aboutall parts of the object are captured in the projection data.Alternatively, partially transmissive density fiducials may be used thatfacilitate detecting the object boundary, but permit a desiredproportion of radiation to penetrate the object.

In one embodiment, the one or more density fiducials are a flexiblematerial that conforms to the shape of the object being imaged. Theflexible material may have a known outer boundary that can beidentified. The one or more density fiducials may also be part of theimaging apparatus designed to hold the object in place. For example, inbreast imaging, a compression mechanism may be positioned to hold andcompress the breast in place. One or more density fiducials adapted tofacilitate identifying the boundary of the object may be affixed to orbe part of the compression mechanism. It should be appreciated that anytype of density fiducial that facilitates identifying the boundary ofthe object may be used, as the aspects of the invention are not limitedin this respect.

In act 1420, projection data is obtained of an object by exposing theobject to radiation from one or more view angles. For example, theprojection data may be obtained from a number of view angles distributeduniformly or non-uniformly about the object. However, the projectiondata may result from a single view angle, as the aspects of theinvention are not limited in this respect. In act 1430, a firstreconstruction is performed on the projection data to form a bootstrapimage of the object. The bootstrap image may be a 2D image, a pluralityof 2D images and/or a 3D image of the object. Since the projection datawas obtained in the presence of the one or more density fiducials,evidence of the density fiducials will be present in the bootstrap image(i.e., the one or more density fiducials will be imaged).

In act 1440, the image of the one or more density fiducials are locatedin the bootstrap image to obtain boundary information indicative of theboundary of the object. For example, the bootstrap imaged may beprocessed and areas of relatively high density characteristic of thedensity fiducials may be identified. The areas of high density are thenconsidered to include locations along the boundary of the object. Thisboundary information may then be used to constrain a secondreconstruction to avoid errors resulting from incorrectly assigningdensity values to locations outside the boundary of the object beingimaged.

In addition to the boundary information derived directly from thedensity fiducials, the boundary may be further defined using othermethods. For example, the boundary of the object between densityfiducials may be approximated using interpolation, by fitting one ormore curves between the density fiducials and/or by using knowninformation about the general shape of the object being imaged. Inaddition, various other image processing techniques may be used todetect more of the object boundary to improve the boundary informationused in the second reconstruction.

For example, edge detection may be used to locate the boundary of theobject. One or more segmentation algorithms may be used to segment theobject to define its boundary. For example, the one or more densityfiducials could be used as a basis for seeding a region growingalgorithm configured to segment the object from non-object material, theborder between the segmented regions operating as the boundary of theobject. In addition, one or more morphological characteristics may beused to locate the boundary. For example, the boundary of a given objectmay have characteristics that result in detectable image properties thatcan be identified during processing of the bootstrap image. For example,in breast imaging, the skin typically results in a characteristicpattern that can be identified by the appropriate image processingalgorithm.

In some embodiments, the boundary may be identified without the aid ofdensity fiducials. For example, act 1410 may not be performed in someembodiments. Instead, the boundary may be identified using morphologicalcharacteristics and/or any other detectable properties of the object inthe image to identify the boundary. For example, in breast imaging, thecharacteristic pattern of the skin may be used to identify the boundary.However, any of various image processing techniques, pattern recognitionand/or computer vision techniques may be used to identify and locate theboundary, as the aspects of the invention are not limited in thisrespect.

In addition, the boundary of an object may be identified manually. Forexample, an operator may indicate the location of density fiducials, thelocation of the boundary, or a combination of both. Manual techniquesmay be performed in combination with automatic techniques to obtainboundary information about the object from the bootstrap image. In someembodiments, instead of identifying boundary information in thebootstrap image, boundary information is identified in the projectiondata (e.g., in each of the 2D projections). A 3D reconstructionalgorithm can then be employed to form a 3D boundary map of from theboundaries identified in each of the projections. This 3D map can thenbe used to constrain a reconstruction of a 3D image. Any one orcombination of techniques may be employed to obtain boundary informationfrom the bootstrap image or the 2D projections, as the aspects of theinvention are not limited in this respect.

In act 1450, the boundary information obtained in act 1440 is used toconstrain a second reconstruction of the projection data. As discussedabove, the lack of knowledge about the boundary of the object may leadto density values being incorrectly assigned outside the object, whichin turn may prevent the density values from being correctly distributedinside the object. Accordingly, the boundary information may be used toinstruct the reconstruction as to where the boundary of the object liesso that density values are not assigned to locations outside the object.

In some embodiments, a zero density value is assigned to each locationoutside the object to initialize the reconstruction. The constraintsimposed by the boundary information may facilitate a reconstruction thatis better posed, reducing the likelihood of the reconstruction algorithmconverging to an undesirable local minimum or otherwise resulting in asolution that does not accurately reflect the density distribution ofthe object (e.g., local minimums where density values are assignedoutside the boundary of the object). It should be appreciated that theboundary information may be used in any way to improve thereconstruction of the projection data, as the aspects of the inventionare not limited in this respect.

Certain imaging procedures, and more particularly, various medicalimaging procedures may have substantial imaging times. For example, animaging interval may include obtaining projection data from a pluralityof view angles, in between which components of the imaging apparatus mayneed to be moved to new locations associated with the corresponding viewangle (e.g., a radiation source and/or detector array may need to berotated about the object being imaged). During the imaging interval, theobject being imaged should remain relatively motionless to preventmotion blur. For example, in medical imaging procedures, motion by ahuman subject during exposure from different view angles may result inprojection data that is misaligned.

Images reconstructed from the misaligned data may appear blurry, orwashed out, and may be unsuitable for diagnostic purposes. The abilityto detect subject motion may be important to timely alert an operatorthat the imaging procedure may need to be repeated. For example, it mayadvantageous to alert an operator that the imaging procedure may need tobe repeated before the patient leaves the medical imaging facility, andpreferably while the patient is still positioned in the imagingapparatus.

The operator of a piece of imaging equipment (e.g., a technician) taskedwith obtaining one or more images of a subject, may not be a radiologistand/or may not be trained in analyzing medical images. Accordingly, bythe time a radiologist can view the images and determine that theimaging procedure needs to be repeated, the subject may have left theimaging apparatus and/or left the facility. Applicant has developedmethods of automatically detecting subject motion to timely alert anoperator without the images having to be inspected. By automaticallydetecting subject motion, an imaging procedure may be repeatedimmediately (e.g., before the subject is removed from the imagingapparatus). In some embodiments, projection data obtained from multipleexposures at the same view angle may be compared to determine whether asubject has moved in the time between the exposures.

FIG. 15 illustrates a method of automatically detecting subject motion,in accordance with some embodiments of the present invention. In act1510, projection data is obtained of a subject from a plurality of viewangles. For example, projection data may be obtained according to any ofthe methods described above, or as described in the '848 patent. As partof obtaining the projection data in act 1510, projection data isobtained from multiple exposures from the same view angle. Exposuresfrom at least one other view angle may be obtained in between themultiple exposures from the same angle such that some finite amount oftime passes between the exposures at the same view angle.

For example, projection data may be obtained initially from a first viewangle. As the imaging procedure continues, projection data may beobtained from a plurality of different view angles according to anydesired exposure plan. For example, projection data may be obtained froma plurality of view angles that are distributed uniformly ornon-uniformly about a portion of the subject being imaged. Afterexposures at each of the plurality of view angles have been performed, asecond exposure may be performed at the first view angle to obtainadditional projection data.

The second exposure at the first view angle need not be performed afterall other exposures have been performed, and more than one repeatexposure may be performed at the first view angle. In addition, therepeat exposures need not be performed at the first view angle, as theaspects of the invention are not limited in this respect. It may bepreferable, however, to take exposures from the same view angle at thebeginning and end of the imaging procedure so that the projection datafrom the repeat exposures are likely to capture subject motionthroughout. A repeat exposure may be obtained in the middle of theprocedure (or at any time) to capture information about subject motionat any desired moment during the imaging procedure.

In act 1520, the projection data obtained from the multiple exposures atthe same view angle are compared to determine if the subject movedbetween exposures. For example, if the subject has not moved or hasmoved negligibly, the projection data at each of the multiple exposuresfrom the same view angle should be substantially the same. However, ifthe subject has moved by any appreciable amount, the projection datawill be different for exposures from the same view angle between whichthe subject moved. In some embodiments, projection data from differentexposures at the same view angle are subtracted from one another. Themagnitude of the difference may be indicative of the extent of thesubject motion. In some embodiments, a correlation is made betweenprojection data obtained from each of the multiple exposures. Highdegrees of correlation will indicate that the subject did not moveappreciably. Likewise, uncorrelated data may indicate subject motion.The projection data from multiple exposures at the same view angle maybe compared in other ways to determine the presence of, or the extent ofsubject motion, as the aspects of the invention are not limited in thisrespect.

In act 1525, it may be determined if there was significant enoughsubject motion to merit repeating the imaging procedure. For example, ifthe magnitude of the difference between projection data obtained frommultiple exposures is above a predetermine threshold, or the projectiondata is too uncorrelated, an alert may be generated to instruct anoperator to perform the imaging procedure again. If the comparison ofthe projection data indicates that there was no or substantially nosubject motion, the projection data may be reconstructed to form one ormore images of the portion of the subject (act 1530). For example, theimaging procedure may be part of a breast examine, and the projectiondata may be reconstructed to form an image of the breast to be analyzedby a radiologist. By automatically detecting subject motion, the breastimaging may be repeated, if need be, before the patient is removed fromthe imaging apparatus and/or leaves the imaging facility.

In some embodiments, motion detection may be achieved without having toobtain multiple exposures at the same view angle. For example,projection data obtained from a plurality of view angles may bereconstructed to form a 3D image. Computed projection data may beobtained by computationally projecting the 3D image onto a plurality of2D planes (e.g., deconstructing the 3D image is a process related to theinverse of image reconstruction). Computing projection data simulatescomputationally the process projecting the object onto the detectors byexposing the object to radiation. The computed projection data may thenbe compared to the observed projection data obtained from exposing theobject from the plurality of view angles. Differences in the computedand observed projection data may be indicative of motion of the subject.For example, a shift in the position of a high-contrast feature betweenthe calculated and observed projection data could be used to identifyobject motion. Alternatively, mathematical operators such as theconvolution or cross-correlation operators could be used to identifyobjection motion.

In another variant of this method, one or more of the observedprojections of the object obtained by exposing the object to radiationat a corresponding view angle may be excluded from the initial 3Dreconstruction. Computed projection data may then be generated thatcorresponds to each of the excluded projections (i.e., computedprojection data may be computed for the view angles from which theobserved projections were excluded). A comparison of the computedprojection data with the excluded observed projections may be used toidentify object motion using the methods described above.

FIG. 16 illustrates an imaging apparatus that may be used to performvarious methods described above, in accordance with some embodiments ofthe present invention. Imaging system 1600 may be suitable, for example,for obtaining projection data to be reconstructed to form 3D images in arelatively low-dose environment, in accordance with various aspects ofthe present invention. Imaging system 1600 may be suitable for obtainingprojection data and reconstructing images according to the variousmethods described in the '848 patent, the '664 application, and/or forperforming any one or combination of methods described in the foregoing.

Imaging system 1600 includes a radiation source 1620, a detector 1630, amotion controller 1640, an image processor 1660 and a display 1690. Theimaging system 1600 can be used to image a single object 1610 or aplurality of objects located within an exposure area 1614. The exposurearea 1614 defines generally the region of space between the radiationsource 1620 and the detector 1630, and is located in the path of theradiation provided by radiation source 1620 in the direction of detector1630. The exposure area 1614 may be the entire region of space locatedin the path of the radiation passing from the radiation source 1620 tothe detector 130, or only a predetermined portion of the space.

Radiation source 1620 may be any component or combination of componentscapable of emitting radiation such as x-ray or gamma radiation. Inimaging system 1600, radiation source 1620 is positioned to emitradiation toward exposure area 1614 such that, when object 1610 ispresent in exposure area 1614, at least some of the radiation impingeson object 1610. In particular, the radiation source 1620 is adapted toemit radiation to form a radiation field 1616, which may be of any shapeor size. In a preferred embodiment, radiation field 1616 is a beam thatradiates outward from a focal point of radiation source 1620substantially in the shape of a cone, and that substantially enclosesobject 1610 within a cone of x-rays during exposures. However, radiationfield 1616 may form other shapes such as a fan beam, pencil beam, etc.,and may be arranged to expose any portion of object 1610, as the aspectsof the invention are not limited in this respect.

Radiation source 1620 is capable of being moved about object 1610 suchthat radiation may be directed at object 1610 from a plurality ofangular positions, i.e., a plurality of view angles with respect toobject 1610 (e.g., as described in further detail below). Detector 1630is positioned to receive at least some of the radiation that passesthrough the exposure area 1614, and in particular, radiation that haspenetrated and exited object 1610. Detector 1630 may be a singledetector, or a detector array disposed continuously or at a plurality ofdiscrete locations. Detector 1630 may be formed from any type ofmaterial responsive to radiation generated by radiation source 1620. Inresponse to impinging radiation, detector 1630 produces signalsindicative of the intensity of radiation impinging on the detectorsurface. Accordingly, recorded intensities of radiation passing throughthe object as represented by the detector signals carry informationabout the absorption characteristics of object 1610, and form, at leastin part, projection data of object 1610.

Detector 1630 may be configured to be moved in correspondence with theradiation source 1620 to detect radiation exiting object 1610 from theplurality of view angles. Motion controller 1640 may be coupled toradiation source 1620 and detector 1630 to cause the rotational movementof the radiation source/detector apparatus such that, as the apparatusrotates about the object, the object remains positioned within theexposure area between the source and detector. Motion controller 1640may be capable of being programmed to move the radiation source anddetector to any desired view angle with respect to object 1610.Together, the radiation source 1620, detector 1630 and motion controller1640 permit projection data of object 1610 to be obtained from any setof view angles. In some embodiments, motion controller 1640 may beprogrammed to control the position of the radiation source and detectorindependently. For example, the motion controller may move the radiationsource and detector along different paths as projection data is obtainedfrom the different view angles, as the aspects of the invention are notlimited in this respect.

In another embodiment, the detector 1630 remains stationary as theradiation source is moved about the object. For example, if the detector1630 is sufficiently large (e.g., a flat panel two-dimensional detectorarray) and/or if the angular range over which projection data isobtained is sufficiently small (e.g., the angular range is limited to arange between 5° and 45° both clockwise and counterclockwise from areference view angle), a single position for the detector 1630 may besufficient to capture projection data from each of the desired viewangles. In addition, in embodiments where detector 1630 remainsstationary, the object may be positioned in direct contact with thedetector.

At each view angle, the detector signal generated by each detector inthe array indicates the total absorption (i.e., attenuation) incurred bymaterial substantially in a line between the radiation source and thedetector. Therefore, the array of detection signals at each view anglerecords the projection of the object onto the detector array at theassociated view angle. For example, using a 2D detector array, theresulting detector signals represent the 2D density projection of theobject on the detector array at the corresponding view angle. Thesignals generated by the detectors form, at least in part, projectiondata (or view data) of the object.

Image processor 1660 may be configured to reconstruct the projectiondata to form images of the object (e.g., 2D or 3D images of the object).Image processor 1660 may be configured to implement any desiredreconstruction algorithm capable of mapping recorded radiation intensityvalues (e.g., detector signals from detector 1630) to correspondingdensity values. Image processor 1660 may also be configured toautomatically process reconstructed images to obtain data from theimages to, for example, modify the projection data and/or inform asubsequent reconstruction of the projection data.

Image processor may be one or more processors located proximate orremote from the radiation source and detector. The image processor maybe configured to execute programs stored on a computer readable mediumsuch as a memory accessible by the image processor. Imaging system 1600may also include a display 1690, such as a monitor, screen and/or otherdisplay device capable of presenting a pixel representation ofreconstructed image data. It should be appreciated that the abovedescribed components are merely exemplary, and any suitable imagingapparatus of any configuration and/or combination of components may beused to implement any one or combination of the methods described above,as the aspects of the invention are not limited in this respect.

The above-described embodiments of the present invention can beimplemented in any of numerous ways. For example, the embodiments may beimplemented using hardware, software or a combination thereof. Whenimplemented in software, the software code can be executed on anysuitable processor or collection of processors, whether provided in asingle computer or distributed among multiple computers. It should beappreciated that any component or collection of components that performthe functions described above can be generically considered as one ormore controllers that control the above-discussed function. The one ormore controller can be implemented in numerous ways, such as withdedicated hardware, or with general purpose hardware (e.g., one or moreprocessor) that is programmed using microcode or software to perform thefunctions recited above.

It should be appreciated that the various methods outlined herein may becoded as software that is executable on one or more processors thatemploy any one of a variety of operating systems or platforms.Additionally, such software may be written using any of a number ofsuitable programming languages and/or conventional programming orscripting tools, and also may be compiled as executable machine languagecode.

In this respect, it should be appreciated that one embodiment of theinvention is directed to a computer readable medium (or multiplecomputer readable media) (e.g., a computer memory, one or more floppydiscs, compact discs, optical discs, magnetic tapes, etc.) encoded withone or more programs that, when executed on one or more computers orother processors, perform methods that implement the various embodimentsof the invention discussed above. The computer readable medium or mediacan be transportable, such that the program or programs stored thereoncan be loaded onto one or more different computers or other processorsto implement various aspects of the present invention as discussedabove.

It should be understood that the term “program” is used herein in ageneric sense to refer to any type of computer code or set ofinstructions that can be employed to program a computer or otherprocessor to implement various aspects of the present invention asdiscussed above. Additionally, it should be appreciated that accordingto one aspect of this embodiment, one or more computer programs thatwhen executed perform methods of the present invention need not resideon a single computer or processor, but may be distributed in a modularfashion amongst a number of different computers or processors toimplement various aspects of the present invention.

Various aspects of the present invention may be used alone, incombination, or in a variety of arrangements not specifically discussedin the embodiments described in the foregoing and is therefore notlimited in its application to the details and arrangement of componentsset forth in the foregoing description or illustrated in the drawings.The invention is capable of other embodiments and of being practiced orof being carried out in various ways. In particular, various aspects ofthe present invention may be implemented in connection with any type,collection or configuration networks. No limitations are placed on thenetwork implementation. Accordingly, the foregoing description anddrawings are by way of example only.

Use of ordinal terms such as “first”, “second”, “third”, etc., in theclaims to modify a claim element does not by itself connote anypriority, precedence, or order of one claim element over another or thetemporal order in which acts of a method are performed, but are usedmerely as labels to distinguish one claim element having a certain namefrom another element having a same name (but for use of the ordinalterm) to distinguish the claim elements.

Also, the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” or “having,” “containing”, “involving”, andvariations thereof herein, is meant to encompass the items listedthereafter and equivalents thereof as well as additional items.

1. A method of imaging an object of interest positioned in an exposurearea, the method comprising: obtaining projection data of the object byproviding radiation from a radiation source to the exposure area anddetecting, by at least one detector, at least some of the radiationexiting the object to form the projection data; performing a firstreconstruction of the projection data to form at least one bootstrapimage; obtaining first data based on information provided by the atleast one bootstrap image including estimating an exit spectrumindicative of the energy spectrum of radiation exiting the object based,at least in part, on density information provided by the at least onebootstrap image; and performing a second reconstruction of theprojection data based, at least in part, on the first data to form atleast one second image.
 2. The method of claim 1, wherein estimating theexit spectrum includes estimating an emission spectrum indicative of theenergy spectrum of radiation emitted by the radiation source.
 3. Themethod of claim 2, wherein estimating the exit spectrum includesmodifying the emission spectrum based on the density information in theat least one bootstrap image to estimate the exit spectrum.
 4. Themethod of claim 1, wherein performing the second reconstruction includesperforming the second reconstruction using the exit spectrum to accountfor at least some beam hardening effects.
 5. The method of claim 1,wherein the first reconstruction is performed assuming that the detectedradiation is substantially of a single energy, and the secondreconstruction is performed assuming that the detected radiationincludes energies distributed according to the exit spectrum.
 6. Themethod of claim 5, wherein further comprising differentiating portionsof the detected radiation contributive by respective energies in theexit spectrum.
 7. The method of claim 6, further comprising, computing,from the detected radiation and based on the exit spectrum, a radiationintensity of radiation at a plurality of energies present in the exitspectrum.
 8. The method of claim 7, wherein the second reconstruction isperformed by reconstructing the radiation intensity for each of theplurality of energies according to a respective attenuation functioncharacteristic of the respective energy.
 9. The method of claim 1,wherein obtaining the first data includes obtaining information aboutlocations of material within the object to facilitate estimating anamount of scattered radiation.
 10. The method of claim 1, whereinobtaining first data includes obtaining boundary information indicativeof a boundary of the object in the at least one bootstrap image.
 11. Themethod of claim 10, wherein performing the second reconstructionincludes using the boundary information to constrain the secondreconstruction.
 12. A method of imaging an object of interest positionedin an exposure area, the method comprising: obtaining projection data ofthe object by providing radiation from a radiation source to theexposure area and detecting, by at least one detector, at least some ofthe radiation exiting the object to form the projection data; performinga first reconstruction of the projection data to form at least onebootstrap image; obtaining first data based on information provided bythe at least one bootstrap image including obtaining information aboutlocations of material within the object to facilitate estimating anamount of scattered radiation; performing a second reconstruction of theprojection data based, at least in part, on the first data to form atleast one second image; dividing an image of the object in the at leastone bootstrap image into a plurality of regions; determining a depth ofeach of the plurality of regions with respect to a reference pointrelated to a radiation source that provides the radiation to theexposure area; estimating an amount of scattered radiation resultingfrom each of the plurality of regions based on the possibility thatradiation passing through the respective region would scatter at theassociated depth; summing the estimates of scattered radiation toprovide an estimate of the total scattered radiation; and modifying theprojection data based, at least in part, on the estimate of the totalscattered radiation.
 13. A method of imaging an object of interestpositioned in an exposure area, the method comprising: obtainingprojection data of the object by providing radiation from a radiationsource to the exposure area and detecting, by at least one detectors, atleast some of the radiation exiting the object to form the protectiondata; performing a first reconstruction of the projection data to format least one bootstrap image; obtaining first data based on informationprovided by the at least one bootstrap image including obtainingboundary information indicative of a boundary of the object in the atleast one bootstrap image, wherein obtaining the boundary informationincludes determining which pixels in the bootstrap image are outside ofthe boundary of the object, and wherein constraining the secondreconstruction includes assigning zero-density values to pixelsidentified as being outside the boundary of the object; and performing asecond reconstruction of the projection data based, at least in part, onthe first data to form at least one second image including using theboundary information to constrain the second reconstruction.
 14. Amethod of imaging an object of interest positioned in an exposure area,the method comprising: obtaining projection data of the object byproviding radiation from a radiation source to the exposure area anddetecting, by at least one detector, at least some of the radiationexiting the object to form the projection data; arranging at least onedensity fiducial in the exposure area, prior to obtaining the projectiondata, such that at least some of the radiation encounters the at leastone density fiducial; performing a first reconstruction of theprojection data to form at least one bootstrap image; obtaining firstdata based on information provided by the at least one bootstrap image;and performing a second reconstruction of the projection data based, atleast in part, on the first data to form at least one second image. 15.The method of claim 14, wherein arranging the at least one densityfiducial includes arranging at least one density fiducial in contactwith the object to demarcate at least a portion of a boundary of theobject.
 16. The method of claim 15, wherein obtaining the first dataincludes obtaining boundary information indicative of a boundary of theobject based at least in part on the image of the at least one densityfiducial in the bootstrap image.
 17. The method of claim 16, whereinreconstruction includes constraining the second reconstruction based onthe boundary information.
 18. The method of claim 17, whereinconstraining the second reconstruction includes assigning zero-densityvalues to regions indicated, by the boundary information, as beingoutside the boundary of the object.